Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity

TL;DR

This paper develops a simplified vector Ginzburg-Landau model to simulate the nonlinear dynamics of light in bulk ENZ media with Kerr nonlinearity, revealing complex wave structures and interactions.

Contribution

It introduces a novel mathematical model for ENZ media with Kerr nonlinearity and demonstrates its application through numerical simulations of complex wave phenomena.

Findings

Observation of nontrivial evolution of symmetric and toroidal wave structures

Demonstration of nonlinear interactions between longitudinal and transverse waves

Validation of the model using split-step Fourier numerical methods

Abstract

A simplified mathematical model is suggested to describe the dynamics of a quasi-monochromatic optical wave in the bulk of an effectively isotropic metamaterial with averaged dielectrical permittivity near zero (ENZ medium), in the presence of a weak spatial nonuniformity, Kerr nonlinearity as well as linear gain due to external pumping. The model is a vector Ginzburg-Landau equation of the general kind, with the dominating curl-curl term in the dispersive operator, and it resembles the equation for electromagnetic waves in plasma [E. A. Kuznetsov, 1974]. In the case of purely real Kerr coefficients, a split-step Fourier method is appropriate for numerical simulations. It makes possible to observe various variants of nontrivial evolution of both central-symmetric and toroidal vector wave structures trapped by a quadratic potential well, as well as nonlinear interaction between the longitudinal and transverse waves in the case of their combination.